A procedure is developed and realized in The form of a numerical mode/ling program for deformation of a gasket in diamond anvils taking account of the effect of high pressure and large elastoplastic strains for the material. The procedure is based on the finite element method with a stepwise iteration algorithm (the initial stress method). In the case of considerable distortion of the finite element network with large strains a procedure is used for redefining the network deformation. A package of programs for solving elastoplastic problems with large strains and high pressure developed at the Institute of Superhard Materials of the Ukrainian National Academy of Sciences is used in the calculations. Two materials are considered: hardened stainless steel T301 and pressed lithographic limestone (PLL). A degree of compression of a factor of eight is achieved for PLL (Odquist parameter q ≈ 5.5, elastic volumetric strain (EVSj 0.7, pressure 24 GPa) and a factor of 5.8 for steel T301 (q ≈ 3, EVS 0.7, pressure 50 G Pa). The distribution of elastic and plastic zones during deformation and stress distribution over the anvil-gasket contact surface are obtained, and the stagewise nature of the deformation process is revealed.